Spatial Patterns in Stage-Structured Populations with Density Dependent Dispersal

Persistent Link:
http://hdl.handle.net/10150/194472
Title:
Spatial Patterns in Stage-Structured Populations with Density Dependent Dispersal
Author:
Robertson, Suzanne Lora
Issue Date:
2009
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Spatial segregation among life cycle stages has been observed in many stage-structured species, including species of the flour beetle Tribolium. Patterns have been observed both in homogeneous and heterogeneous environments. We investigate density dependent dispersal of life cycle stages as a mechanism responsible for this separation. By means of mathematical analysis and numerical simulations, we explore this hypothesis using stage-structured, integrodifference equation (IDE) models that incorporate density dependent dispersal kernels.In Chapter 2 we develop a bifurcation theory approach to the existence and stability of (non-extinction) equilibria for a general class of structured integrodifference equation models on finite spatial domains with density dependent kernels. We show that a continuum of such equilibria bifurcates from the extinction equilibrium when it loses stability as the net reproductive number n increases through 1. We give several examples to illustrate the theory.In Chapter 3 we investigate mechanisms that can lead to spatial patterns in two dimensional Juvenile-Adult IDE models. The bifurcation theory shows that such patterns do not arise for n near 1. For larger values of n we show, via numerical simulation, that density dependent dispersal can lead to the segregation of life cycle stages in the sense that each stage peaks in a different spatial location.Finally, in Chapter 4, we construct spatial models to describe the population dynamics of T. castaneum, T. confusum and T. brevicornis and use them to assess density dependent dispersal mechanisms that are able to explain spatial patterns that have been observed in these species.
Type:
text; Electronic Dissertation
Keywords:
Density dependent dispersal; Integrodifference Equations; Segregation of life cycle stages; Spatial patterns; Tribolium
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Cushing, Jim M
Committee Chair:
Cushing, Jim M

Full metadata record

DC FieldValue Language
dc.language.isoENen_US
dc.titleSpatial Patterns in Stage-Structured Populations with Density Dependent Dispersalen_US
dc.creatorRobertson, Suzanne Loraen_US
dc.contributor.authorRobertson, Suzanne Loraen_US
dc.date.issued2009en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractSpatial segregation among life cycle stages has been observed in many stage-structured species, including species of the flour beetle Tribolium. Patterns have been observed both in homogeneous and heterogeneous environments. We investigate density dependent dispersal of life cycle stages as a mechanism responsible for this separation. By means of mathematical analysis and numerical simulations, we explore this hypothesis using stage-structured, integrodifference equation (IDE) models that incorporate density dependent dispersal kernels.In Chapter 2 we develop a bifurcation theory approach to the existence and stability of (non-extinction) equilibria for a general class of structured integrodifference equation models on finite spatial domains with density dependent kernels. We show that a continuum of such equilibria bifurcates from the extinction equilibrium when it loses stability as the net reproductive number n increases through 1. We give several examples to illustrate the theory.In Chapter 3 we investigate mechanisms that can lead to spatial patterns in two dimensional Juvenile-Adult IDE models. The bifurcation theory shows that such patterns do not arise for n near 1. For larger values of n we show, via numerical simulation, that density dependent dispersal can lead to the segregation of life cycle stages in the sense that each stage peaks in a different spatial location.Finally, in Chapter 4, we construct spatial models to describe the population dynamics of T. castaneum, T. confusum and T. brevicornis and use them to assess density dependent dispersal mechanisms that are able to explain spatial patterns that have been observed in these species.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectDensity dependent dispersalen_US
dc.subjectIntegrodifference Equationsen_US
dc.subjectSegregation of life cycle stagesen_US
dc.subjectSpatial patternsen_US
dc.subjectTriboliumen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorCushing, Jim Men_US
dc.contributor.chairCushing, Jim Men_US
dc.contributor.committeememberWatkins, Josephen_US
dc.contributor.committeememberTabor, Michaelen_US
dc.identifier.proquest10383en_US
dc.identifier.oclc659752001en_US
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